State Of Cuprate Superconductors Research Articles

Thermodynamics of the pseudogap in cuprates

The key thermodynamic characteristics of the pseudogap state in cuprate superconductors are reviewed. These include YBa2Cu3O7−δ, Y0.8Ca0.2Ba2Cu3O7−δ, YBa2Cu4O8, Bi2Sr2CaCu2O8+δ, La2−xSrxCuO4, and Tl2Ba2CuO4. The electronic specific heat was extracted using a differential technique, and the evolution of the specific-heat coefficient γ and electronic entropy S as a function of temperature, doping, and magnetic field reveals a canonical behavior summarized by the following. The normal-state gap which opens in the pseudogap domain apparently remains open to the highest temperatures investigated. The gap decreases in magnitude with increasing doping and closes abruptly at a critical doping of p ≈ 0.19 holes/Cu, independent of temperature. In this picture, the pseudogap is separated from the pseudogap-free region of the phase diagram by a vertical line similar to the vertical line separating the incoherent and coherent antinodal quasiparticle states found in ARPES. The important role of fluctuations is evident by a diverging enhancement of γ(T) on either side of Tc, and this enables extraction of the mean-field transition temperature Tcmf>Tc, defining a crescent of parapairing above Tc(p) which extends across the entire superconducting phase diagram and which is quite distinct from pseudogap phenomenology. The data are consistent with d-wave pairing and the BCS ratios are extracted, revealing canonical near-weak-coupling behavior across the over-doped region with a sudden suppression occurring at p ≈ 0.19 when the pseudogap sets in.

Компьютерное моделирование наноскопических фазово-неоднородных состояний и фазовых диаграмм ВТСП купратов и никелатов

More than 35 years of experience in the study of cuprate superconductors shows that the main characteristics of the phase diagram can only be obtained by taking into account mesoscopic static/dynamic phase inhomogeneity as a key property of these materials. Within a minimal model for the CuO2 planes with the on-site Hilbert space reduced to only three effective valence centers [CuO4]7-,6-,5- (nominally Cu1+,2+,3+) with different conventional spin and different orbital symmetry we propose a unified non-BCS model that allows one to describe the main features of the phase diagrams of doped cuprates within the framework of a simple effective field theory. Using Maxwell's construction, the global nature of the electronic phase separation in the CuO2 planes of HTSC cuprates is established, which makes it possible to understand and explain many fundamental features of the physics of the normal and superconducting state of cuprates, including the mechanism of formation of the HTSC and pseudogap phase. The features of phase-inhomogeneous states and their evolution with temperature and doping degree, including the special role of the impurity potential in cuprates/nickelates with nonisovalent substitution, are considered for particular examples of the charge triplet model in the framework of the classical Monte Carlo method.

Computer simulation of nanoscopic phase-inhomogeneous states and phase diagrams of HTSC cuprates and nickelates

More than 35 years of experience in the study of cuprate superconductors shows that the main characteristics of the phase diagram can only be obtained by taking into account mesoscopic static/dynamic phase inhomogeneity as a key property of these materials. Within a minimal model for the CuO2/NiO2 planes with the on-site Hilbert space reduced to only three effective valence centers [CuO4]7-,6-,5- (nominally Cu1+,2+,3+) with different conventional spin and different orbital symmetry we propose a unified non-BCS model that allows one to describe the main features of the phase diagrams of doped cuprates within the framework of a simple effective field theory. Using Maxwell's construction, the global nature of the electronic phase separation in the CuO2 planes of HTSC cuprates is established, which makes it possible to understand and explain many fundamental features of the physics of the normal and superconducting state of cuprates, including the mechanism of formation of the HTSC and pseudogap phase. The features of phase-inhomogeneous states and their evolution with temperature and doping degree, including the special role of the impurity potential in cuprates/nickelates with nonisovalent substitution, are considered for particular examples of the charge triplet model in the framework of the classical Monte Carlo method. Keywords: cuprates, nickelates, effective field theory, phase diagram, phase separation, Monte-Carlo.

Explanation of Non-linear In-Plane Resistivity and Hall Coefficient in the Normal State of Cuprates: Polaronic Approach

We present a theoretical study of the in-plane resistivity ρ a b (T) and Hall coefficient R H (T) within the polaronic model and precursor pairing scenario by considering a two-component charge carrier picture in the normal state of high-temperature superconducting cuprates (HTSC). Here, we use a Boltzmann-equation approach and extended BCS-like model to compute ρ a b (T) and R H (T) in the τ-approximation. The opening of the pseudogap (PG) in the normal state of the cuprates should affect their transport properties. We have found that the transition to the PG regime and the effective conductivity of charge carriers in the normal state are responsible for the pronounced non-linear temperature dependence of ρ a b and R H . With the two-component model analysis, we conclude that the opening of the BCS-like PG, while the non-linear temperature dependence of ρ a b and R H could be understood as a consequence of pairing fluctuations in the PG state of cuprate superconductors. The calculated results for ρ a b (T) and R H (T) were compared with the experimental data obtained for various hole-doped cuprates. For all the considered cases, a good quantitative agreement was found between theory and experimental data. We also show that the energy scales of the binding energies of charge carriers are identified by PG crossover temperature on the cuprate phase diagram.

Competing Unconventional Charge-Density-Wave States in Cuprate Superconductors: Spin-Fluctuation-Driven Mechanism

To understand the origin of unconventional charge-density-wave (CDW) states in cuprate superconductors, we establish the self-consistent CDW equation, and analyze the CDW instabilities based on the realistic Hubbard model, without assuming any $q$-dependence and the form factor. Many higher-order many-body processes, which are called the vertex corrections, are systematically generated by solving the CDW equation. When the spin fluctuations are strong, the uniform $q=0$ nematic CDW with $d$-form factor shows the leading instability. The axial nematic CDW instability at $q = Q_a = (\delta,0)$ ($\delta \approx \pi/2$) is the second strongest, and its strength increases under the static uniform CDW order. The present theory predicts that uniform CDW transition emerges at a high temperature, and it stabilize the axial $q = Q_a$ CDW at $T = T_{CDW}$. It is confirmed that the higher-order Aslamazov-Larkin processes cause the CDW orders at both $q = 0$ and $Q_a$.

A wave packet approach to interacting Fermions

In this thesis, we study the breakdown of the Fermi liquid state in cuprate superconductors using the renormalization group (RG). We seek to extend earlier work on the crossover from the Fermi liquid state to the pseudo gap phase based on RG flows in the so-called saddle point regime. Progress in the derivation of effective models for the conjectured spin liquid state has been hindered, by the difficulties involved in solving the strong coupling low energy Hamiltonian. We tackle the problem by introducing an orthogonal wave packet basis, the so-called Wilson-Wannier (WW) basis, that can be used to interpolate between the momentum space and the real space descriptions. We show how to combine the WW basis with the RG, such that the RG is used to eliminate high-energy degrees of freedom, and the remaining strongly correlated system is solved approximately in the WW basis. We exemplify the approach for different one-dimensional model systems, and find good qualitative agreement with exact solutions even for very simple approximations. Finally, we reinvestigate the saddle point regime of the two-dimensional Hubbard model. We show that the anti-nodal states are driven to an insulating spin-liquid state with strong singlet pairing correlations, thus corroborating earlier conjectures.

Change of carrier density at the pseudogap critical point of a cuprate superconductor.

The pseudogap is a partial gap in the electronic density of states that opens in the normal (non-superconducting) state of cuprate superconductors and whose origin is a long-standing puzzle. Its connection to the Mott insulator phase at low doping (hole concentration, p) remains ambiguous and its relation to the charge order that reconstructs the Fermi surface at intermediate doping is still unclear. Here we use measurements of the Hall coefficient in magnetic fields up to 88 tesla to show that Fermi-surface reconstruction by charge order in the cuprate YBa2Cu3Oy ends sharply at a critical doping p = 0.16 that is distinctly lower than the pseudogap critical point p* = 0.19 (ref. 11). This shows that the pseudogap and charge order are separate phenomena. We find that the change in carrier density n from n = 1 + p in the conventional metal at high doping (ref. 12) to n = p at low doping (ref. 13) starts at the pseudogap critical point. This shows that the pseudogap and the antiferromagnetic Mott insulator are linked.

Electron Correlation and Impurity-Induced Quasiparticle Resonance States in Cuprate Superconductors

We theoretically study the quasiparticle resonance states around a nonmagnetic impurity in cuprate superconductors based on t-t'-J-U model. The purpose of introducing the Coulomb repulsive interaction U is to partially impose the double occupancy constraint by employing the Gutzwiller projected mean-field approximation. We determine the spatial variation of the order parameter and the local density of states (LDOS) by self-consistently solving Bogoliubov-de Gennes equations. We find that in the large U limit, a zero-energy resonance peak in the LDOS indeed appears for the impurity potential in the unitary limit, at the same time the asymmetric superconducting coherence peaks are strongly suppressed. As U decreases the electron double occupancy d is permitted and gradually increases, leading to the decreasing of order parameter. In particular the above zero-energy resonance peak begins to evolve into a double-peaked structure since a critical value $d_{c}$. These important feathers are qualitatively agreement with the scanning tunneling spectroscopy experiments, and uncover the essential role played by the electron correlation in cuprate superconductors.

Reply to “Comment on ‘Diamagnetism and Cooper pairing aboveTcin cuprates' ”

We analyze recent torque measurements of the magnetization $M_d$ vs. magnetic field $H$ in optimally doped YBa$_2$Cu$_3$O$_{7-y}$ (OPT YBCO) to argue against a recent proposal by Rey et al that the magnetization results above $T_c$ are consistent with Gaussian fluctuations. We find that, despite its strong interlayer coupling, OPT YBCO displays an anomalous non-monotonic dependence of $M_d$ on $H$ which represents direct evidence for the locking of the pair wavefunction phase $\theta_n$ at $T_c$ and the subsequent unlocking by a relatively weak $H$. These unusual features characterize the unusual nature of the transition to the Meissner state in cuprate superconductors. They are absent in low-$T_c$ superconductors to our knowledge. We also stress the importance of the vortex liquid state, as well as the profiles of the melting field $H_m(T)$ and the upper critical field curve $H_{c2}(T)$ in the $T$-$H$ plane. Contrary to the claims of Rey et al, we show that the curves of the magnetization and the Nernst signal illustrate the inaccessibility of the $H_{c2}$ line near $T_c$. The prediction of the $H_{c2}$ line by Rey et al is shown to be invalid in OPT YBCO.

The mystery and the mystique

'Mottness' or a reconstructed Fermi surface? Nodes and arcs, or pockets? Both approaches to the pseudogap state of cuprate superconductors receive some support from specific heat data obtained up to 45 T. Can the two be reconciled?

Overdoping effect on pair breaking peak energy in the electronic Raman spectra of high-Tc cuprate superconductors

In the superconducting state of cuprates we have measured electronic Raman spectra (ERS) and plotted the pair breaking energy as a function of hole concentration in overdoped regime. The target materials in this study are Ca-substituted YBCO and Tl2201, both of which have similar Tc when it is optimally doped but different number of CuO2 planes in the unit cell. For both materials pair breaking peak energy (Eb) shows decrease with increasing carrier concentration. Interestingly Eb seems to show a rapid drop at a certain carrier concentration, where several measurements suggest the signature of quantum critical point. The similarity of the ERS between the two materials indicates that the behavior is not affected by the number of CuO2 planes in a unit cell, and that electronic state of cuprates may have a remarkable change at the critical hole concentration.

On the Role of Polarization of Oxygen Ions and Mechanism of Superconductivity in Cuprate Superconductors

A new approach to the valence electron state in cuprate superconductors leading to a new mechanism of high-temperature superconductivity is considered. The approach takes into account specific features of the outer electron shells of the compound-forming elements and polarization of anions by cations. The polarization of anions by copper cations results in sharing of a valence electron by every two neighboring ions, which gives rise to a highly correlated state of the valence electrons and formation of a localized spin-ordered electron lattice responsible for dielectric and magnetic properties of an undoped material. It is also shown that asymmetric polarization of an anion by cations with inert gas shells transforms an unshared anion electron pair into a superconducting one by exciting it into a hybrid state. The superconducting state of the material itself results from formation and delocalization of one-dimensional Wigner crystals of the excited pairs.

ELECTRONIC STRUCTURE OF KINETIC ENERGY DRIVEN CUPRATE SUPERCONDUCTORS

In this paper, we review the low energy electronic structure of the kinetic energy driven d-wave cuprate superconductors. We give a general description of the charge-spin separation fermion-spin theory, where the constrained electron is decoupled as the gauge invariant dressed holon and spin. In particular, we show that under the decoupling scheme, the charge-spin separation fermion-spin representation is a natural representation of the constrained electron defined in a restricted Hilbert space without double electron occupancy. Based on the charge-spin separation fermion-spin theory, we have developed the kinetic energy driven superconducting mechanism, where the superconducting state is controlled by both superconducting gap parameter and quasiparticle coherence. Within this kinetic energy driven superconductivity, we have discussed the low energy electronic structure of the single layer and bilayer cuprate superconductors in both superconducting and normal states, and qualitatively reproduced all main features of the angle-resolved photoemission spectroscopy measurements on the single layer and bilayer cuprate superconductors. We show that the superconducting state in cuprate superconductors is the conventional Bardeen-Cooper-Schrieffer like with the d-wave symmetry, so that the basic Bardeen-Cooper-Schrieffer formalism with the d-wave gap function is still valid in discussions of the low energy electronic structure of cuprate superconductors, although the pairing mechanism is driven by the kinetic energy by exchanging spin excitations. We also show that the well-pronounced peak-dip-hump structure of the bilayer cuprate superconductors in the superconducting state and double-peak structure in the normal state are mainly caused by the bilayer splitting.

Nodal and antinodal gaps in the superconducting state of cuprates

We present an electronic Raman scattering study of a mercury-based single layer cuprate, as a function of both doping level and temperature in the superconducting state. On the deeply overdoped side, we show that the antinodal gap is a true superconducting gap. In contrast, on the underdoped side, our results reveal the existence of a break point close to optimal doping below which the antinodal gap is gradually disconnected from superconductivity.

Finite-size and pressure effects inYBa2Cu4O8probed by magnetic-field penetration-depth measurements

We explore the combined pressure and finite-size effects on the in-plane penetration depth \lambda_{ab} in YBa_2Cu_4O_8. Even though this cuprate is stoichiometric the finite-size scaling analysis of \lambda_{ab}^{-2}(T) uncovers the granular nature and reveals domains with nanoscale size L_{c} along the c-axis. L_{c} ranges from 33.2 Angstrom to 28.9 Angstrom at pressures from 0.5 to 11.5 kbar. These observations raise serious doubts on the existence of a phase coherent macroscopic superconducting state in cuprate superconductors.

Spin susceptibility in the superconducting state of cuprates

An analytic expression for the spin susceptibility in the superconducting state is derived taking into account strong correlation effects and the temperature dependence of the transverse nuclear spin–spin relaxation rates is calculated for both s- and d-wave pairing symmetries.

Chiral symmetry breaking and phase fluctuations: AQED3theory of the pseudogap state in cuprate superconductors

A d-wave superconductor, its phase coherence progressively destroyed by unbinding of vortex-antivortex pairs, suffers an instability related to chiral symmetry breaking in two-flavor QED$_3$. The chiral manifold exhibits large degeneracy spanned by physical states acting as inherent ``competitors'' of d-wave superconductivity. Two of these states are associated with antiferromagnetic insulator and ``stripe'' phases, known to be stable in the pseudogap regime of cuprates near half-filling. The theory also predicts additional, yet unobserved state: a d+ip phase-incoherent superconductor.

Anomalous microwave conductivity due to collective transport in the pseudogap state of cuprate superconductors

and underdoped YBa2Cu3O6.5 is found to be anomalous in that Rs(T.Tc)fiXs(T.Tc) in the pseudogap state. This implies plasmonlike response and negative permittivities «8(v),0 at microwave frequencies indicating non-Fermi-liquid transport in the ab plane. The anomalous microwave response is shown to arise from a collective mode characterized by a plasma frequency v pCM;0.1 eV and extremely low damping G CM ;10 25 ‐10 24 eV, distinctly different from those observed at optical frequencies.

Probing the singlet character of the two-hole states in cuprate superconductors

Using spin-resolved resonant photoemission we have probed the singlet vs. triplet character of the two-hole state in the layered cuprates Bi2Sr2CaCu2O8+δ,La2−xSrxCuO4 and Sr2CuO2Cl2. The combination of the photon circular polarization with the photoelectron spin detection gives access to the character of the photoemission final states, which correspond to the two-hole configurations localized at a (CuO4) site. In particular, the lowest energy state is found to have a very high singlet character in all the measured compounds. This can be considered as a strong indication of the existence and stability of the so-called Zhang–Rice singlets in the layered cuprates.

A novel approach to the polaronic metallic state of cuprate superconductors and the d-wave pairing mechanism

The present novel approach consists of two stages: in the first stage the many-electron states of a CuO6 octahedron or a CuO5 pyramid are calculated by the first-principles variational method, by taking into account the local distortions of a CuO6 octahedron or a CuO5 pyramid. In the second stage a metallic state is constructed in the presence of the local AF ordering constructed by the localized spins. In this metallic state the local distortions are treated in the mean field approximation, so that a “pseudopolaronic effect” is taken into account. Based on this approach, the hole-concentration dependence of Tc and the isotope effect are calculated for LSCO, and compared with experimental results. This approach leads to d-wave pairing mechanism.